A curious example of two model categories and some associated differential graded algebras

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Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators,and, as a by-product, recover the known graphs E4, E6 and E8 describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.

Analysing the impact of public capital stock using the NEG wage equation: a panel data approach

This paper examines the relationship between the level of public infrastructure and the level of productivity using panel data for the Spanish provinces over the period 1984-2004, a period which is particularly relevant due to the substantial changes occurring in the Spanish economy at that time. The underlying model used for the data analysis is based on the wage equation, which is one of a handful of simultaneous equations which when satisfied correspond to the short-run equilibrium of New Economic Geography theory. This is estimated using a spatial panel model with fixed time and province effects, so that unmodelled space and time constant sources of heterogeneity are eliminated. The model assumes that productivity depends on the level of educational attainment and the public capital stock endowment of each province. The results show that although changes in productivity are positively associated with changes in public investment within the same province, there is a negative relationship between productivity changes and changes in public investment in other regions.

Neuroscience, quantum indeterminism and the Cartesian soul.

Quantum indeterminism is frequently invoked as a solution to the problem of how a disembodied soul might interact with the brain (as Descartes proposed), and is sometimes invoked in theories of libertarian free will even when they do not involve dualistic assumptions. Taking as example the Eccles-Beck model of interaction between self (or soul) and brain at the level of synaptic exocytosis, I here evaluate the plausibility of these approaches. I conclude that Heisenbergian uncertainty is too small to affect synaptic function, and that amplification by chaos or by other means does not provide a solution to this problem. Furthermore, even if Heisenbergian effects did modify brain functioning, the changes would be swamped by those due to thermal noise. Cells and neural circuits have powerful noise-resistance mechanisms, that are adequate protection against thermal noise and must therefore be more than sufficient to buffer against Heisenbergian effects. Other forms of quantum indeterminism must be considered, because these can be much greater than Heisenbergian uncertainty, but these have not so far been shown to play a role in the brain.

Selection bias and unobservable heterogeneity applied at the wage equation of European married women

This paper utilizes a panel data sample selection model to correct the selection in the analysis of longitudinal labor market data for married women in European countries. We estimate the female wage equation in a framework of unbalanced panel data models with sample selection. The wage equations of females have several potential sources of.

Characteristic reflection patterns in the southeast Canadian cordillera, northern Appalachians and Swiss Alps

There are some striking similarities and some differences between the seismic reflection sections recorded across the fold and thrust belts of the southeast Canadian Cordillera, Quebec-Maine Appalachians and Swiss Alps. In the fold and thrust belts of all three mountain ranges, seismic reflection surveys have yielded high-quality images of. (1) nappes (thin thrust sheets) stacked on top of ancient continental margins; (2) ramp anticlines in the hanging walls of faults that have ramp-flat or listric geometries; (3) back thrusts and back folds that developed during the terminal phases of orogeny; and (4) tectonic wedges and regional decollements. A principal result of the Cordilleran and Appalachian deep crustal studies has been the recognition of master decollements along which continental margin strata have been transported long distances, whereas a principal result of the Swiss Alpine deep crustal program has been the identification of the Adriatic indenter, a crustal-scale wedge that caused delamination of the European lithosphere. Significant crustal roots are observed beneath the fold and thrust belts of the Alps, southeast Canadian Cordillera and parts of the southern Appalachians, but such structures beneath the northern Appalachians have probably been removed by post-orogenic collapse and/or crustal attenuation associated with the Mesozoic opening of the Atlantic Ocean.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Lp theory for the multidimensional aggregation equation

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A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

A functional equation related to the product in a quadratic number field

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